LOCALIZATION ALGORITHMS FOR WIRELESS SENSOR NETWORK SYSTEMS

Transcription

1 The Pennsylvania State University The Graduate School Department of Computer Science and Engineering LOCALIZATION ALGORITHMS FOR WIRELESS SENSOR NETWORK SYSTEMS A Thesis in Computer Science and Engineering by Xiang Ji c 2004 Xiang Ji Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2004

2 The thesis of Xiang Ji was reviewed and approved by the following: Hongyuan Zha Associate Professor of Computer Science and Engineering Thesis Adviser Chair of Committee John J. Metzner Professor of Computer Science and Engineering Wang-Chien Lee Associate Professor of Computer Science and Engineering Peng Liu Assistant Professor of Information Science and Technology Raj Acharya Professor of Computer Science and Engineering Chairman, Department of Computer Science and Engineering Signatures are on file in the Graduate School.

3 iii Abstract Advances in the micro-electro-mechanical system and wireless communication technology have enabled researchers to develop large-scale wireless sensor networks with a large number of inexpensive and small sensors. Many applications are developed based on wireless sensor networks, such as habitat monitoring, navigation, and objects detection and tracking. By its nature, location awareness is indispensable for the implementation of these applications. In this dissertation, we study two issues related to sensor and object localization in wireless sensor networks. We first examine the sensor localization algorithms, which are used to determine sensors positions in ad-hoc sensor networks. Most existing sensor localization methods suffer from various location estimation errors that result from ranging errors, complex network topologies and anisotropic terrain, etc. We explore the characteristics of dimensionality reduction techniques and propose three sensor localization algorithms based on the multidimensional scaling techniques. They include a centralized sensor localization algorithm, a distributed sensor localization algorithm, and a robust sensor location algorithm based on multidimensional scaling. The results of our experiment demonstrate that these algorithms are effective in positioning sensors Positioning all sensors in a sensor network usually consumes a large amount of time and energy. In many applications based on sensor networks, there is no need to estimate the location of all sensors in a sensor network. Sometimes, only sensors within a given direction or region need to be located. We propose the concept of differentiated

4 iv sensor localization. Three differentiated sensor localization methods are also proposed, which can selectively locate only one or a specific set of sensors. Given the sensor location information known, many surveillance tasks may then be carried out with sensor networks. One of the major applications of sensor networks is locating objects and tracking their movement. We investigate the problem of using large-scale sensor network to locate large continuous objects and track their boundary movement. The large continuous objects, such as wild fire and bio-chemical materials, are different from the traditional single or multiple discrete targets in that they are continuously distributed across a region and usually occupy a large area. Detecting and tracking the large continuous objects poses many challenging research issues which have not been adequately addressed in previous research. Capturing their spread and boundary information is usually an efficient approach for monitoring them. A distributed algorithm is proposed in this research to locate the boundary of continuous objects. A dynamic structure is proposed to track the movement of boundaries and to facilitate the fusion and dissemination of boundary information in a sensor network. Simulation results show the efficiency of the proposed algorithms.

5 v Table of Contents List of Figures ix Acknowledgments xv Chapter 1. Introduction Wireless Sensor Networks Applications of Sensor Networks Location-aware Computing Localization in Sensor Networks Dissertation Overview Chapter 2. Background and Related Research Wireless Sensor Network Model Elements of Localization Received Signal Strength Indication Time of Arrival Time Difference of Arrival Angle of Arrival Triangulation Trilateration Multilateration Related Research

6 2.4 Challenges of Localization vi Chapter 3. Sensor Localization with Multidimensional Scaling Problem Definition Overview of The Centralized Sensor Localization Multidimensional Scaling Classical Multidimensional Scaling Iterative Multidimensional Scaling Ranging Estimation Pairwise Distance Collection Performance Study Summary Chapter 4. Distributed and Robust Sensor Localization Distributed Sensor Localization Calculating Relative Positions Aligning Relative Positions Robust Sensor Localization Performance Study Simulation Model Results Summary Chapter 5. Differentiated Sensor Localization

7 vii 5.1 Introduction Related Work Challenges Differentiated Sensor Localization Methods The Localization-Along-Curve Method The Localization-Within-Region Method On Demand Sensor Localization Method Performance Evaluation Simulation Model Results Summary Chapter 6. Large Continuous Object Detection and Tracking Introduction Related Work Model Assumptions and Challenges Boundary Localization Boundary Sensors Selection Distributed Boundary Localization Boundary Movement Tracking Curvilinear Belt Structure and Its Partitioning Tracking Boundaries Performance Evaluations

8 viii Simulation model Evaluation criteria Results Summary Chapter 7. Conclusions and Future Work Summary Future Research References

9 ix List of Figures 2.1 Example of tiny wireless sensor node [41] Sensors deployed in the mountain area form an ad-hoc sensor network and monitor the environment Soldiers with receivers scout the enemy tanks information with the assistance of a distributed sensor network [101] The power of the received radio signal strength attenuates exponentially with the increase of distance between the transmitter and receiver Triangulation Trilateration Multilateration A sensor network deployed in a square area with obstacles A sensor network in non-square area Irregular radio pattern of a sensor Anisotropic terrain condition leading to different radio ranges Hop distance and signal strength Routes of a flooding initialized by node S Flooding routes from a source node of a sensor network A broadcast initialized by node S collects 34 pairwise distances A broadcast initialized by node S collects 24 pairwise distances A broadcast initialized by node S collects 34 pairwise distances

10 x 3.7 (a)the physical positions of sensors in an adjacent area.(b) The recovered relative positions of sensors in the adjacent area based on classical MDS. (c) These sensors physical positions after alignment. (d)when the error of measured distances for pairwise adjacent sensors increases, the error rates of estimated sensor positions increase (a)error rates of sensor localization increase when the percentage of sensor pairwise distances collected and the number of iteration increase. (b)when the collected pairwise distance and the number of iteration are fixed, the error rates of sensor localization increase with the increase of distance measurement error Error rates when varying the percentage of collected pairwise distances Percentage of collected pairwise distances when increasing the number of source nodes and broadcasts Flooding from a starting anchor to the whole network. Red nodes are anchor nodes Position estimation in the adjacent area of a starting anchor sensor The propagation of position estimation Classical multidimensional scaling Iterative multidimensional scaling Error rates when applying the robust localization method with anchor sensors to all sensors in a square region with an uniform radio range and different distance measurement errors

11 xi 4.7 Errors when applying the robust localization method with anchor sensors to all sensors in a square region with different signal attenuation factors (radio ranges) The propagation of sensor localization along the route from sensor A to sensor B Position estimation in the adjacent area of a sensor without position known Localization error rates within an isotropic square area Localization error rates within an anisotropic square area Localization error rates within a T-shape area Errors when applying the distributed on demand localization method to one sensor in two square regions with uniform and different signal attenuation factors, respectively Large continuous objects and their boundaries; The boundary information may either be collected by a fixed sink or be scouted/queried by mobile users, such as a soldier (a) Possible cases of boundary estimation by boundary sensors, among which pair (S1, B) and (S1, C) are error prone. We try to eliminate the two pairs by reducing the range of neighborhood to ad c. (b) Selecting boundary sensors: Only sensors are covered by the continuous object and marked by the small ellipses are boundary sensors

12 xii 6.3 Distributed boundary estimation: E, F, G, and H are boundary sensors; They form five boundary pairs with non-boundary sensors A, B, C, and D, respectively; Five position marked with small circles are estimated as the boundary locations Curvilinear belt structure for object boundary and its partition: The large continuous object is on the left side of the object boundary. Black dots are sensors that detect the object, and those dark dots along the entity boundary (A, B, C) are boundary sensors. Small circles are sensors that do not detect the object. Most boundary sensors are connected to the backbone (B, A, D, C). Boundary sensor A is the head of the partition. A and C are two boundary sensors, and they are out of each others radio range. An ellipse is formed with A and C as foci, and α is its eccentricity Ellipse α values for a randomly and uniformly deployed sensor network tend to be a constant Curvilinear belt partition reconstruction and d r ; Boundary moves to left with speed V. When boundary is close enough to the margin of the current partition, head A will select sensor B as a new head to construct a new partition

13 xiii 6.8 (a)when the number of sensors deployed in the 1000m-by-1000m field increases from 1000 to 4000, the error rates of estimated boundary decrease. (b)when the number of sensors deployed in the 1000m-by-1000m field increases from 1000 to 4000, the total number of boundary sensors involved in boundary estimation increases (a)when hop distance of sensors increases from 30m to 70m, the error rates of estimated boundary decrease. (b)when hop distance of sensors increases from 30m to 70m, the number of selected boundary sensors keeps constant with compactness distance applied. The number of boundary sensors increase if they are selected based on hop distance (a)when the rectangle object s right boundary moves from 300 to 600, the error rates of estimated boundary are stable. (b)when the rectangle object s right boundary moves from 300 to 600, the numbers of boundary sensors of estimated boundary are stable (a)the error rates of the estimated boundary for a circle object are relatively constant when its radius increase. (b)the number of boundary sensors involved in a circle object boundary estimation are increasing approximately linearly with the length of the boundary (a)when a increases from 1 to 2, error rates of estimated boundary increase. (b) When a increases from 1 to 2, the number of boundary sensors involved in boundary estimation increases Shortest path from sensors to the sink in the baseline case

14 xiv 6.14 (a)total message costs during boundary travelling from 0 to 300 with different speeds. (b)total message costs during boundary travelling from 0 to 180 with different number of partitions of the curvilinear belt structure. (c)total message costs during boundary travelling from 0 to 180 with different hop distances. (d)total message costs during boundary travelling from 0 to 180 with curvilinear belt structure in different width. 117

15 xv Acknowledgments No words in the world can be used to express my gratitude to my thesis advisor, Dr. Hongyuan Zha. The work presented here could not possibly have been accomplished without the help and encouragement of my advisor. He gave me the opportunity to jump into an amazing research field with a rare chance to discover the truth of the world. He gave me a great deal of freedom in my research, but I am never lacked for help when it was needed. I am especially indebted for the financial support which he has provided to me over the years. Dr. Hongyuan Zha has guided and influenced me. He is an excellent researcher and maintains the highest standards for himself and his students. He is also an awesome advisor and grants me his careful teaching, large doses of guidance, patience, encouragement. He has developed me the spirit of always pursuing for high quality research. He taught me how to identify a problem that will substantially impact the current state-ofthe-art research, the society, the industry and the ecology. He also showed me that strong theoretical foundation and cross-discipline knowledge are indispensable to perform solid research. Under his edification, I finally found my career. I hope I can inherit and live up to his high standards in my future career. I also feel very grateful to other committee members, Dr. John J. Metzner, Dr. Wang-Chien Lee and Dr. Peng Liu. I thank them for serving on my qualifying exam and dissertation committees. Their suggestions have greatly improved my dissertation work.

16 xvi I would like to specially thank Dr. John J. Metzner, for his inspiration and enlightening discussions on a wide variety of topics. His invaluable insight on my research work has helped me make significant improvements on this dissertation work. He is very attentive, responsive, always has the best interests of his students at heart. He is always very kind to me. Special thanks also due to Dr. Wang-Chien Lee. He gave me many important suggestions some leading to a research topic in my dissertation. He also carefully polished my papers and gave me very valuable comments. I appreciate Dr. Wang-Chien Lee for his comprehensive and insightful knowledge on mobile data management research and other related fields. I always enjoy the discussion with him and the classes he offered. Dr. Peng Liu has been extremely generous with his time, patient and support than I probably deserve. He thoughtfully asked questions which made me look at my proposed research from different perspectives. My appreciation for his sharp mind in research grows each time I interact with him. I feel very grateful and indebted to him. I would like to thank lots of people for having contributed, in one way or another, to the completion of this thesis. Last but not least, I thank my parents, my brother, my sister and my wife for their love and support, their unconditional encouragement and belief during these years.

17 1 Chapter 1 Introduction 1.1 Wireless Sensor Networks With the advances in the miniaturization and integration of sensing and communication technologies, large-scale wireless sensor networks with a large number of low-cost and low-power sensors have been developed. In a wireless sensor network, hundreds or even thousands of tiny, battery-powered sensor nodes are scattered throughout a physical area. Each sensor in the sensor network collects data, for instance, sensing vibration, temperature, radiation and other environmental factors. These sensors relay the collected data to their neighboring sensors and then to a specified destination where the data are processed. This sensory input is used to describe the surroundings in real time. One typical application scenario is that hundreds or thousands of sensors are randomly deployed within a battle field or urban area to detect intrusion or to monitor the distribution of target objects and materials, such as animals, vehicles, wild fire, or bio-chemical materials. In the last decade, we have witnessed the bloom of the Internet, which provides us with the ability to transfer diverse forms of information readily and thus revolutionizes business, industry, science, education, and our lifestyles. Wireless sensor networks represent a new way of computing. They have been envisioned as a proactive computing world in which networked computing nodes automatically acquire real-time data about a

18 2 physical environment. They may, in the long run, be equally significant as the Internet by providing measurements of our physical environment, leading to our understanding and ultimately, to the utilization of this information for a wide range of applications. These sensor networks will eventually help us to improve lives, promote a better understanding of the world and make people more productive. 1.2 Applications of Sensor Networks Wireless sensor networks have the unique features of easy deployment, self organization and fault tolerance. Emerging as a new information-gathering paradigm, wireless sensor networks have been used in a broad range of applications relating to health care, environmental control, energy, food safety, and manufacturing [6, 5, 28, 54]. During the past several years, there have been many to turn the vision of sensor networks into a reality. Some prototypes of sensor nodes have been developed, including Motes [39, 42] at Berkeley, uamps [35, 68] at MIT, and GNOMES [98] at Rice. The elementary functions of sensor networks include localization, detection, tracking, and targeting. Besides military applications, civilian applications have been developed based on these elementary functions, which can be classed into habitat monitoring, environment observation, health and other commercial applications. In addition, Sibley et al. have recently developed mobile sensors, known as Robomote, which are equipped with wheels and are able to move within a field [88]. Applications in sensor deployment and coverage are studies based on mobile sensors [45, 46]. As one of the first efforts of utilize sensor networks for civil applications, Berkeley and Intel Research Laboratory used a Mote sensor network to monitor storm petrels on

19 3 Great Duck Island, Maine [65] in the summer of Thirty-two sensor nodes were deployed on a small island off the coast of Maine to collect useful live data onto the world wide web. The system operated for over four months and provided data for two months after researchers had left the island for the winter due to poor weather conditions. This habitat monitoring application represents an important class of sensor network applications. Most importantly, sensor networks are able to collect data under hazardous conditions which are not directly accessible to human beings. During the storm petrel monitoring research, a set of system design requirements were raised, including the hardware design of the nodes, the design of the sensor network, and the capabilities for remote data access and management. Many efforts have been made to address these system design requirements, which have led to the development of a set of prototype sensor network systems. The sensor network used in the Berkeley and Intel research, although still primitive, efficiently collected the interesting habitat data and provided researchers studying storm petrel with valuable information. Sensor networks have found their application in environment observation and forecasting. A real-world example of such an application is the system of Automated Local Evaluation in Real-Time (ALERT) developed by the National Weather Service with wireless sensor networks [1]. Equipped with a meteorological/hydrological sensing device, the sensors in this system usually measure several properties of the local weather, such as water level, temperature, and wind. Data are transmitted via line-of-sight radio communication from the sensors to the base station. A Flood Forecast Model has been adopted to process these data and issue an automatic warning. Web-based query is available, so that the system is able to provide important real-time rainfall and water level

20 4 information to evaluate the possibility of potential blooding anywhere in the country. Currently ALERT is deployed across most of the western United States, and it is heavily used for flood warnings in California and Arizona. Sensor networks have recently been introduced to health care with applications ranging from patients and doctors tracking and monitoring [5], glucose level monitors, cancer detectors, even to artificial organ [87, 86, 12, 93]. Scientists have proposed that biomedical sensors are implanted into human body for different purposes. These sensors communicate with an external computer system through wireless interface. Multiple biomedical sensors are networked into an application-specific solution to diagnose and treat diseases. The biomedical sensors offer the promise of significantly advances in medical care. 1.3 Location-aware Computing The paradigm of context-aware computing [94, 75, 8] has become increasingly interesting to researchers lately. Context-aware computing systems aim to autonomously change their function based on their observation of the environment around them. By determining the context or environment, the computing devices are able to adjust themselves to the current computing demands, customize their behavior according to their location, or even actively react to their surroundings. The paradigm of context-aware computing represents a significant step towards the vision of ubiquitous computing [37, 95, 58]. Location-aware computing [38] is an important and practical subset of the contextaware computing paradigm. Fundamental to the computing in these systems is location

21 5 awareness. By detecting and tracking the locations of objects, it is feasible to derive other useful location related information, such as the objects orientation and mobility. The behavior of location-aware computing systems depends heavily on these types of location information. Since these location-aware computing systems are usually embedded into the physical world, it is necessary to establish spatial relationships between these computing devices and their physical environment. For example, many of these sensor network systems are designed to monitor or control the behavior of the physical world where they are deployed, which means that the sensor nodes of these systems often need to determine their actions based on their physical locations or spatial relationship with the particular objects. Therefore, the location information of the sensors and target objects is indispensable for the management and operation of sensor networks. 1.4 Localization in Sensor Networks The issue of localization has been raised and addressed in many research fields, including the autonomous robot and vehicle navigation [43, 97] for mobile robotics [91], virtual reality systems [96], and user location and tracking in cellular networks [89]. Determining the physical positions of sensors is a fundamental and crucial issue for wireless ad-hoc sensor network operations for several reasons. Sensor networks are often developed in the form of a layered network protocol stack. In the application layer, sensor localization is necessary for location-aware applications that process data based on location [32]. In order to use the data collected by sensors, it is often necessary to have their position information stamped. For example, to detect and track objects with sensor networks, the physical position of each sensor is needed for identifying the positions of

22 6 detected objects. In the network layer, many communication protocols of sensor networks are built upon the knowledge of the geographic positions of sensors [15, 17, 101]. For example, knowledge of location information and transmission range enables geographic routing algorithms that propagate information through multi-hop sensor networks [78, 77, 57]. However, in most cases, sensors are deployed without their position information being known in advance, so there is no supporting infrastructure available to locate them after deployment. It is therefore necessary to find some approaches for identifying the location of each sensor in wireless sensor networks after their deployment. One of the most well known and widely used technologies for localization is the Global Positioning System (GPS) [97]. Many applications have been developed based on GPS. Although it is possible to find the position of each sensor in a wireless sensor network with the aid of GPS installed in each sensor, it is not practical to use GPS for sensor localization for three reasons. Firstly, GPS is not always available because of the line of sight conditions. For instance, it does not work indoors, under water, or in a subway. Secondly, since a typical GPS receiver costs approximately one hundred dollars, it is too expensive to equip each sensor with a GPS receiver, considering that these sensors are usually designed to be low cost and disposable. Finally, the GPS receivers are highly power-consuming while the sensors are designed to require low-power and therefore to ensure their greater longevity. Based on the previous discussion, alternative sensor localization systems are required. Considering the application scenarios of sensor networks, designing localization systems for sensor networks is more challenging than designing localization systems for

23 7 applications in many other domains. Sensors are designed to be small and to require low computation power and a limited power supply. They are usually randomly and densely deployed within a large region. After being deployed, these sensors self-organize into a distributed ad-hoc sensor network. The ideal sensor localization system is also required to have a low computation and a low power cost. The localization system should be able to tolerate ad-hoc deployment without infrastructure support for localization, and should be able to perform self-localization. The localization system is expected to scale to include a large number of sensor nodes, and must accommodate a dynamic environment and system. 1.5 Dissertation Overview The rest of this dissertation is divided into six chapters. In Chapter 2, we present the necessary background information and related research for sensor localization in distributed ad-hoc sensor networks. The challenges for effective and robust sensor localization are also discussed. In Chapter 3, we present a centralized sensor location method based on multidimensional scaling technique. It utilizes pairwise sensor distances to recover locations of sensors in two (or three) dimensions. If pairwise distances between all sensors are known, a simple eigen-decomposition will generate the sensors locations. In this chapter, we focus on the case of only a portion of pairwise sensor distances known and an iterative calculation of the optimal sensors locations. The method yields competitive location results.

24 8 In Chapter 4, the centralized sensor localization method is extended to a distributed sensor localization algorithm and a robust sensor localization algorithm. They are developed based on multidimensional scaling technique to deal with diverse challenging conditions. In the distributed sensor localization algorithm, multidimensional scaling and coordinate alignment techniques are applied to recover positions of adjacent sensors. The estimated positions of the anchors are compared with their true physical positions and corrected to achieve robust sensor localization. This method is demonstrated to be able to achieve robust sensor localization under diverse challenging conditions such as complex terrain. In Chapter 5, we propose the concept of differentiated sensor localization in distributed ad-hoc sensor networks. The application demands for differentiated sensor localization are identified. Then, three differentiated sensor localization methods based on multidimensional scaling techniques are proposed to get accurate position estimation and to reduce computation and communication costs. They are able to locate only one or a specific set of sensors based on demand. In Chapter 6, the application of locating large continuous objects and tracking their movement is proposed and investigated. Large continuous objects are different from collections of discrete targets such as a group of vehicles in that they are continuously distributed across a region and occupy a large area. Locating their spatial extents and related boundary information represents a class of very challenging tasks in sensor network research. We first propose a distributed algorithm for locating the boundary information of large continuous objects covered by a sensor network. Further, a dynamic curvilinear belt structure is proposed to track the movement of boundaries in real-time

25 9 manner and to facilitate the fusion and dissemination of boundary information in a sensor network. In Chapter 7, we first summarize the contributions of this dissertation on localization algorithms for wireless sensor network systems. Then, we examine potential extension based on the proposed approaches. Finally, we discuss some directions for future work.

26 10 Chapter 2 Background and Related Research 2.1 Wireless Sensor Network Model Advances in the miniaturization and integration of sensing and communication technologies have facilitated the development of large-scale wireless sensor networks with hundreds or even thousands of tiny, battery-powered sensors. Figure 2.1 shows the tiny sensors [39, 42, 41]. In a sensor network, hundreds or even thousands of such kind of sensors are scattered throughout a physical area. Each sensor in the sensor network collects data, for instance, sensing vibration, temperature, humidity and other environmental factors. The sensor relays the collected data to its neighboring sensors and then to a specified destination where they are processed. For example, the Figure 2.2 illustrates that sensors are deployed in the mountain area to monitor the environment. Another typical application scenario is that of a large number of sensors deployed within some battle fields or urban areas to monitor the intrusion or distribution of target objects and materials, such as enemy vehicles, wild fire, or bio-chemical spill materials. In Figure 2.3, soldiers scout the enemy tanks information with the assistance of a distributed sensor network [101]. In the general model of wireless ad-hoc sensor networks, a large number of sensors are deployed within a given area without pre-assigning their locations. Each sensor

27 11 Fig Example of tiny wireless sensor node [41]. usually combines the functionality of sensing, radioing and processing, and it typically has a limited power supply and low mobility. Communications between the sensors are through omni-directional radioing. Since each sensor has limited signal strength, only neighboring sensors within a specific hop distance are able to directly communicate with each other. Non-neighboring sensors communicate through hop-by-hop relay. In general, the costs for computation locally are much lower than those for communication among sensors. In order to prolong the life of a wireless sensor network, it is desirable to minimize the communication costs in designing sensor network protocols and algorithms. The distance between a pair of sensors can be estimated based on radio signal strength measurement (RSSI), time of arrival for ultrasound (TOA), time difference of arrival (TDOA), and angle of arrival (AoA) with smart antenna. Based on the measured distances, sensors have their locations estimated with some localization algorithms, such

28 12 as trilateration, multilateration, or other location bound information [14, 17, 33, 71, 83, 80]. In a sensor network, there are usually one or a few sensors that have a strong radio signal and can communicate with a distant base station. These are named as sinks and play the role of gateway for information exchange between the sensor networks and the outside world. Collected information by the sensor network may either be aggregated by several sinks and relayed to external servers or the Internet, or be queried by some mobile users in the network. In the following parts of the dissertation, we use sink to represent both fixed sinks and mobile users. In the general model of wireless ad-hoc Fig Sensors deployed in the mountain area form an ad-hoc sensor network and monitor the environment. sensor network, there are usually some landmarks or nodes named anchor nodes, whose

29 position information is known, within the area to facilitate locating all sensors in a sensor network. 13 Fig Soldiers with receivers scout the enemy tanks information with the assistance of a distributed sensor network [101]. 2.2 Elements of Localization Most localization methods first estimate distances or angles between unknown sensors and anchor sensors, then the location of unknown sensors are calculated with some geometry algorithms. Thus, the most important elements for sensor localization are distance measurement, angle measurement, and geometry constraints. In the following section, we discuss available techniques for each of them.

30 Received Signal Strength Indication During radio propagation, an important characteristic is that the radio signal attenuates as the distance between the transmitter and receiver increases. The power of the received radio signal falls off exponentially with distance increasing, and the receiver can measure this attenuation based on Received Signal Strength Indication (RSSI) in order to estimate the distance to the sender. RSSI measures the power of the signal at the receiver. Based on the transmit power, the propagation loss is calculated and the loss can be translated into distance estimate. This method has been used mainly for radio frequency (RF) signals. In [76], radio propagation models are well researched, and they are used to predict the average RSSI at a given distance away from the transmitter. An ideal radio propagation model, P r (d) = P λ G t G r λ2 4π 2 d n L, (2.1) predicts the received signal power as a function of the distance between the transmitter and the receiver. In the ideal model, P λ is the transmitted power, G t is the antenna gains of the transmitter, G r is the receiver, L is the system loss, and λ is the system wavelength. Usually G t, G r, and L can be set as 1 [13, 15, 16, 14]. In [83], the distance estimation with received RF signal strength using the WINS sensor nodes [3] is studied. In the experiments, different configuration strategies, including different power levels in transmitters and deployment strategies of sensors, are used to estimate the relation between received signal strength and distance between transmitter

31 and receiver. The power of the received radio signal strength attenuates exponentially with the increase in distance as seen in Figure Fig The power of the received radio signal strength attenuates exponentially with the increase of distance between the transmitter and receiver Time of Arrival The distance between the transmitter and the receiver may be estimated based on the speed of the wave propagation and the measured time for a radio signal to travel between two sensor nodes. The method may be applied to many different signals, such as RF, acoustic, infrared and ultrasound. The implementation of the technique depends on the measurement of time of arrival (ToA). The ToA may be measured with some advanced timing techniques.

32 16 The Global Positioning System (GPS) uses the technique for distance estimation [97]. In GPS, each satellite (transmitter) transmits a unique code. On the receiver side, a copy of the code is created. The receiver gradually shifts its internal clock to correspond to the received code, which is called lock-on. Once a receiver has locked-on to a satellite, the receiver determines the exact time of receiving radio signal from the satellite. Based on the time, the ToA can be determined by subtracting the known transmission time from the calculated receive time. ToA offers a high level of accuracy, but also requires relatively fast processing capabilities in sensor nodes to resolve many timing differences for fine-grained measurements Time Difference of Arrival The distance from transmitter to receiver may be measured by the time difference of arrival (TDoA) of different communication media at different speeds. For example, the measurement for time of arrival (ToA) is made based on two different modalities of communication, ultrasound and radio, in sensor nodes. The propagation speeds for ultrasound and radio are considerably different. Then, the radio signal is used for synchronization between the transmitter and the receiver and the ultrasound signal is used to estimate the distance between them. The TDoA technique is used in projects of Active Bat [92], AHLoS [83], Cricket [74], and Cricket Compass [75].

33 Angle of Arrival Angle of Arrival (AoA) means the angle at which signals are received by the receiver from the transmitter. An Angle of Arrival system is able to estimate the angle at which signals are received and to use simple geometric relationships to estimate the relative locations of transmitter and receiver. Angles of Arrival may also be combined with distance estimates to derive relative locations. The implementation of the AoA system relies on smart antenna with antenna arrays to measure the angle at which the signal arrives. A smart antenna is an array of antenna elements connected to a digital signal processor. Such a configuration will not only enable AoA estimation, but also will dramatically enhance the capacity of wireless links through the combination of diversity gain, array gain, and interference suppression. There are two major disadvantages of the AoA techniques which make it inapplicable to sensor networks, however. First, the cost of the complex antenna array is high. Second, the AoA techniques will not scale well for systems with a large number of such nodes Triangulation Triangulation is a geometric technique that uses the angles of arrival to determine the location of sensors. With the angle of each anchor sensor, with respect to the unknown sensor node in some reference frame, the unknown sensor node s locations are calculated with the trigonometry laws of sines and cosines. The computation of triangulation is illustrated by Figure 2.5 [80].

34 18 Fig Triangulation Trilateration Trilateration is a geometric technique that uses distances between three anchor sensors and one unknown sensor to determine the unknown sensor s location. An unknown sensor is uniquely located when at least three reference points are associated with it in a two-dimensional space. The location of the unknown sensor is estimated by calculating the intersection of three circles. Figure 2.6 illustrates the computation geometry constraint [83] Multilateration An unknown sensor s location may also be estimated with multilateration with its distances to more than three anchor sensors. In [9], Beutel studied the multilateration with the least square algorithm.

35 19 Fig Trilateration. For n anchor sensors in three dimensional space and their distances to the unknown sensor, we have d 2 1 d d 2 n = (x 1 u x ) 2 + (y 1 u y ) 2 (x 2 u x ) 2 + (y 2 u y ) 2... (x n u x ) 2 + (y n u y ) 2, (2.2) where d i is the distance between the ith anchor sensor and the unknown sensor, (x i, y i, z i ) is the location of ith anchor sensor in three-dimensional space, and (u x, u y, u z ) is the location of unknown sensor in three-dimensional space.

36 20 The equation can be converted into the following relations through linear operations: Au = b, (2.3) A = 2 (x 1 x n ) (y 1 y n ) (x 2 x n ) (y 2 y n ) (x n 1 x n ) (y n 1 y n ), (2.4) u = u x u y, (2.5) b = d 2 1 d2 n x2 1 + x2 n y2 1 + y2 n d 2 2 d2 n x2 2 + x2 n y2 2 + y2 n... d 2 n 1 d2 n x2 n 1 + x2 n y2 n 1 + y2 n. (2.6)

37 21 The u can be derived with [29, 34] u = (A A) 1 A b. (2.7) Figure 2.7 illustrates the computation geometry constraint [83]. Fig Multilateration. 2.3 Related Research In the robotics research community, many methods have been discovered for robotic localization. Howard et al. used maximum likelihood to estimate a mobile

38 22 robot s location [44]. Roumeliotis et al. proposed a distributed Kalman filter for cooperative localization [79]. Fox et al. proposed probabilistic collaborative localization [27]. There have been many efforts to deal with the sensor localization problem. They mainly fall into one of the following four classes or a combinations of them. The first class of methods improved the accuracy of distance estimation by using different signal techniques. The Received Signal Strength Indicator (RSSI) technique was employed to measure the power of the signal at the receiver. Relatively low accuracy is achieved in this way. However, because of its simplicity, RSSI has been widely used in previous research. Later, Time of Arrival (ToA) and Time Difference of Arrival (TDoA) were used by Savvides et al. [83, 19] and Priyantha et al. [74] to reduce the errors of range estimation, but these methods require equipping each sensor node with a powerful computation capability. Recently, Niculescu et al. used Angle of Arrival (AoA) to measure the positions of sensors [71]. The AoA sensing requires each sensor node to be installed with an antenna array or ultrasound receivers. The second class of sensor localization methods relies on a large number of sensor nodes with positions known densely distributed in a sensor network [15, 16, 14]. These nodes with positions known, which are also named as beacons or anchor nodes, are arranged in a grid across the network to estimate other nodes positions nearby them. The third class of localization methods employs distance vector exchange to find the distances from the non-anchor nodes to the anchor nodes. Based on these distances, each node can estimate its position by performing a trilateration or multilateration [70, 83]. The performance of the algorithms is deteriorated by range estimation

39 23 errors and inaccurate distance measures, which are caused by complex terrain and the anisotropic topology of the sensor network. Savarese [80] tried to improve the above approach by iteratively computing. However, this method adds a large deal to the communication cost of the algorithm and still cannot generate a good position estimation in some circumstances. Moreover, the accuracy of this class of algorithms relies on the average radio range estimation, and it tends to deteriorate when the topology of a sensor network is anisotropic. For example, in Figure 2.8, sensors are deployed in a square area. A Building C C B Fig A sensor network deployed in a square area with obstacles But there are some buildings that are marked by shadowed rectangle areas, and sensors cannot access them. Thus, the routes between a pair of sensors are severely detoured severely by the buildings in the square area, and the estimated distances of AC and BC are increased significantly. There is a similar situation happens to the case in Figure 2.9, when sensors are deployed in a T-shape area, instead of in a square area which is

40 24 C C A B Fig A sensor network in non-square area assumed and used as the fundamental condition by most existing research works. A and B are two anchors, A may estimate radio range with the distance of AB and hop count in the route from A to B. If A and B estimate their distances to C with the estimated radio range, the estimated distances will be increased a lot by error. Another example is that the ideal radio range of a sensor is a circle centered in the sensor. However, a sensor usually has an irregular radio pattern, which is represented with the black curve in Figure 2.10, in real world. This meas that the radio range of a sensor is different at different directions. In Figure 2.11, sensors are deployed on a square area with deep grass or bushes on the left-hand part and clear ground on the right. The complexity of the terrain leads to different signal attenuation factors and radio ranges in the field. The last class of methods [17, 70, 81] locally calculates maps of adjacent nodes with trilateration or multilateration and pieces them together to estimate the nodes

41 25 maximum radio range sensor Fig Irregular radio pattern of a sensor C D A r 1 r 2 Grass B Clear ground Fig Anisotropic terrain condition leading to different radio ranges

42 26 physical or relative positions. The performance of these algorithms relies heavily on the average radio range estimation and suffers from the cumulative range error during the map stitching. Recently, there has been some research on the error characteristics of sensor localization [82, 72] and computation complexity [7]. Chintalapudi analyzed factors that impact the performance of the system and then proposed ad-hoc localization systems with ranging and either bearing or imprecise bearing information [21]. Eren applied graph rigidity theory to locate sensors [25]. Range constraints [24] and area constraints [33] are used to locate sensors in coarse granularity as well. 2.4 Challenges of Localization Considering the real sensor network application scenario, there are several challenges in designing effective and robust sensor localization algorithms. Firstly, since a large number of sensors are generally used when they are randomly deployed across an given area, we hope to achieve good position estimation as well as keep the hardware design of sensors simple and inexpensive. Secondly, in many circumstances it is impossible to get a large number of anchor nodes deployed uniformly across the area to assist the location estimation of non-anchor nodes. Thus, it is desirable to design a sensor localization method that is able to generate accurate localization estimation with as few anchors as possible. Thirdly, sensors may be deployed in battle fields or in urban areas with complex terrain and vegetation (Figure 2.8, Figure 2.9). The sensor network may have a high level of anisotropicity (Figure 2.11). However, most existing research studies that have

43 27 explored sensor localization algorithms are based on isotropic network topology in a square area. Neither their algorithms nor their experimental environment dealt with a sensor network that has had an anisotropic topology as seen in Figure 2.8, Figure 2.9, Figure 2.10, and Figure Fourthly, most of previous methods estimate an average hop distance and broadcast it to whole network. In many cases, sensors may be deployed on an area with anisotropic vegetation and terrain conditions (Figure 2.11). Thus, sensors at different locations in the area may have different radio ranges, and using a uniform radio range calculation will lead to serious errors during sensor localization (in [70, 83, 80]) and such errors may propagate throughout the sensors in the network [17, 81]. Finally, as we have mentioned, most existing sensor localization research tries to provide accurate location estimation for a network of sensors. Wireless sensor networks have limited energy availability, while sensor localization usually involves energyconsuming computation and communication. Therefore, it is always desirable to reduce the energy costs for sensor localization. Among many approaches that have been used to reduce energy caused by sensor localization, one of the most effective method is to eliminate sensor localization or to reduce the times of localization. So, it is necessary to develop localization methods that are able to locate sensors only on demand for energyefficiency concerns. We also noticed that many applications and operations in sensor networks only require the location information of some sensors. This situation enables on demand sensor localization. Some sensor networks are mobile or deployed in a dynamic environment, for example, sensor networks deployed in a river or sea to monitor fish activities or water pollution. They tend to slowly and constantly drift with water

44 28 current. Estimated locations of sensors are invalidated quickly. In this case, it is difficult to locate all sensors in the sensor network. Instead, it is preferable to locate the right sensors at the right time.

45 29 Chapter 3 Sensor Localization with Multidimensional Scaling Most existing localization algorithms make use of trilateration or multilateration based on range measurements obtained from TOA, TDOA and RSSI. We explore the idea of using dimensionality reduction techniques to estimate sensors coordinates in two (or three) dimensional space. In this chapter, we present a centralized sensor localization algorithm based on a dimensionality reduction technique - Multidimensional Scaling. It utilizes pairwise sensor distances to recover locations of sensors in two (or three) dimensions. If pairwise distances between all sensors are known, a simple eigen-decomposition will generate sensors locations. In this chapter, we focus on the case of only a portion of pairwise sensor distances known and iterative calculation of the optimal sensors locations. The method yields competitive location results and has the feature of providing location estimations with various accuracies according to users requirement or power-budget. 3.1 Problem Definition In order to estimate all sensors location in a distributed wireless ad-hoc sensor network, a small percentage of sensors have their location information known either

46 30 through manual configuration or equipped with GPS. These sensors with location information known are referred as anchor sensors and other sensors without location information are defined as unknown sensors. We hope to estimate all sensors locations with the assistance of anchor sensors. In general, the anchor sensors broadcast their locations to their neighbors. Neighboring unknown sensors measure their spatial relation from their neighbors and use the broadcasted anchor sensor locations to estimate their own positions. For an unknown sensor, once an unknown node estimates its position, it becomes an anchor sensor and is able to assist other unknown sensors to estimate their locations. 3.2 Overview of The Centralized Sensor Localization In addition to improving the accuracy of location estimation and reducing algorithm costs as previous research, a requirement-aware and power-aware sensor location algorithm based on multidimensional scaling technique is proposed, which provides location estimation with various accuracies based on power budget and application requirement. Firstly, a portion of pairwise distances of sensors are collected through flooding in a sensor network. Then, an iterative multivariate optimization algorithm is performed based on these pairwise distances to generate relative locations for nodes. The accuracy of the locations depends on the number of pairwise distances collected. If more pairwise distances are collected, higher accuracy is achieved when calculating nodes relative location while less pairwise distances lead to more errors in sensor location. We can collect more pairwise distance by initializing more flooding operation in sensor networks, which

47 31 will consume more power of sensors in the network. So there is tradeoff between the accuracy of the location estimation and the power consumption of the sensor network. The users may determine the accuracy based on their requirements and the current power budget of the sensor network. At last, three anchor nodes within the network are used to convert the relative positions computed above into physical positions. The location algorithm requires centralized computation, which means some sensors collecting and transmitting pairwise distance information to a computer or sensor. The paradigm is supported by sensor system design [40] or fly-over base-station, and has been used by Doherty et al. [24] in their sensor position algorithm. In the work, we focus on the location estimation aspect instead of communication protocol details. The advantages of our approach are: various accuracies of sensor locations can be achieved based on different power budget and accuracy requirement for a wireless sensor networks by launching different number of broadcasting through the network. For each node whose location is unknown, instead of utilizing its distances to limited number of anchor nodes or neighboring nodes in previous research, we use its distances to many other nodes to optimally locate it and reduce errors in distance measurement. Second, instead of finding the location of nodes one by one with tendency of error cumulation, we calculate the locations of nodes simultaneously and globally with high tolerance of range estimation error and inaccurate distance measures. At last, three anchor nodes that are not in a line are enough for our algorithm to identify absolute positions of all nodes. In this dissertation, we illustrate the algorithm with planar networks and it can be easily adapted into 3-D cases.

48 The main steps in our method are collecting pairwise distances and estimating sensor locations with multidimensional scaling technique Multidimensional Scaling The multidimensional scaling (MDS) refers to a set of methods that is widely used in behavioral, econometric, and social sciences to analyze subjective evaluations [11, 30, 84]. We use it as a data-analytic approach to discover the dimensions that underlie the judgements of distance and model data in a geometric space. The main advantages in using the MDS for position estimation is that once calculation with MDS generates all involved sensors location information, and it always generates relatively high accurate position estimation even based on limited and error-prone distance information. There are several varieties of MDS. We focus on classical MDS and the iterative optimization of MDS, the basic idea of which is to assume that the dissimilarity of data are distances and then deduce their coordinates Classical Multidimensional Scaling If all pairwise distances of sensors in an ad-hoc sensor network are collected, we can use the classical multidimensional scaling method to estimate the positions of sensors. T = [t ij ] n 2 denotes the true locations of the set of n sensor nodes in 2-dimensional space. d ij (T) stands for the distance between sensor i and j based on their position in T and 2 d ij (T) = ( (t ia t ja ) 2 ) 1/2. (3.1) a=1

49 33 If we define H = TT, then d ij (T) 2 = t 2 ik + t 2 ik 2 t ik t jk = H ii + H jj 2H ij. (3.2) Without loss of generality, we center the data at the coordinate matrix T. Then, n H ij = 0. i=1 By sum equation 3.2 over i, over j, and over both i and j, we get: 1 n 1 n n d 2 ij = 1 n H n ii + H jj, (3.3) i=1 i=1 n d 2 ij = 1 n H n jj + H ii, (3.4) i=1 j=1 1 n 2 n n d 2 ij = 2 n H n ii. (3.5) i=1 j=1 i=1 Now from equation 3.2, we get H ij = 1 2 [H ii + H jj d2 ij ] = 1 2 [1 d 2 n ij + 1 d 2 n ij d2 ij 1 n j i 2 d 2 ij ] (3.6) i j

50 That means the H can be calculated with d ij. Since H = TT, H is needed to be factorized. With eigen-decomposition, 34 H = UV U, (3.7) where U = [u 1, u 2,..., u n ] and V = diag(v 1, v 2,..., v n ]). In order to get equation 3.7, A is re-scaled as X = UV 1 2 = [u 1 v 1 21, u 2 v 1 22,..., u n v 1 2 n ], (3.8) and H = XX. The X is different from T in that X is n n and T is n 2. Just take the first two coordinates in X as T. Based on the above, the classical multidimensional scaling method is summarized as: 1. Compute the matrix of squared distance D 2, where D = [d ij ] n n ; 2. Compute the matrix J with J = I e e T /n, where e = (1, 1,...,1); 3. Apply double centering to this matrix with H = 1 2 JD2 J; 4. Compute the eigen-decomposition H = UV U T ; 5. Suppose we want to get the i dimensions of the solution (i = 2 in 2-D case), we denote the matrix of largest i eigenvalues by V i and U i the first i columns of U. 1 The coordinate matrix of classical scaling is X = U i V 2 i.

51 35 The computation complexity of classical MDS is an O(N 3 ) [11] Iterative Multidimensional Scaling If only a portion of pairwise distances for sensors in an ad-hoc sensor network are collected, we can use the iterative multidimensional scaling method to estimate the positions of sensors. T = [t ij ] n 2 denote the true locations of the set of n sensor nodes in 2-dimensional space. If not all pairwise distances of sensors in T are collected, we use the iterative multidimensional scaling algorithm to estimate sensors location. d ij (T) stands for the distance between sensor i and j based on their position in T and 2 d ij (T) = ( (t ia t ja ) 2 ) 1/2. (3.9) a=1 The collected distance between node i and j is δ ij. If we ignore the errors in distance measurement, δ ij is equal to d ij (T). We will discuss the error effects to location estimation caused by differences between δ ij and d ij (T) later. If only a portion of pairwise distances are collected, some δ ij are undefined for some i, j. In order to assist computation, we define weights w ij with value 1 if δ ij is known and 0 if δ ij is unknown and assume δ ij = d ij (T) in the following induction. X = [x ij ] n 2 denotes the estimated locations of the set of n sensor nodes in 2-dimensional space. X is randomly initialized as X [0] and will be updated into X [1], X [2], X [3]... to approximate T with our iterative algorithm. d ij (X)

52 means the calculated distance between sensor i and j based on their estimated positions 36 in X and m d ij (X) = ( (x ia x ja ) 2 ) 1/2. (3.10) a=1 We hope to find the a position matrix X to approximate T by minimizing σ(x) = i<j w ij (d ij (X) δ ij ) 2. (3.11) This is a quadratic function without constraints. The minimum value of such functions is reached when its gradient is equal to 0. For our problem, we have the following observations: σ(x) = w ij δ 2 ij + w ij d 2 ij (X) 2 w ij δ ij d ij (X), (3.12) i<j i<j i<j w ij d 2 ij (X) = tr(x (w ij A ij )X) = tr(x ( w ij A ij )X) = tr(x V X) (3.13) i<j i<j i<j where where A ij is a matrix with a ii = a jj = 1, a ij = a ji = 1, and all other elements zeros, V = i<j w ij A ij, tr the trace function and w ij δ ij d ij (X) = w ij δ ij ( m a=1 (x ia x ja ) 2 ) 1/2 ( m a=1 (t ia t ja ) 2 ) 1/2 d ij (T)

53 37 w ij δ ij ( m a=1 (x ia x ja )(t ia t ja )) d ij (T) = w ij δ ij tr(x A ij T) d ij (T) = tr(x ( w ij δ ij d ij (T) A ij )T) where the equality achieved when X = T. Thus, we get σ(x) = w ij δ 2 ij + tr(x V X) 2tr(X ( w ij δ ij d i<j ij (X) A ij )X) w ij δ 2 ij + tr(x V X) 2tr(X ( w ij δ ij d i<j ij (T) A ij )T), and the equality is achieved when X = T. This means that the derivative of the right side of the inequation is zero when the equality is achieved. Based on the above idea, we easily induce the update formular of the SMACOF algorithm V X = ( w ij δ ij d ij (T) A ij )T, (3.14) or X = V 1 ( w ij δ ij d ij (T) A ij )T. (3.15) If V 1 does not exist, we should replace it with Moore-Penrose inverse of V given by V = (V + 11 ) 1 n (3.16)

54 38 In summary, the distances between some pairs of sensors in the local area are not available. When this happens, the iterative MDS is employed to compute the relative coordinates of adjacent sensors. We summarize the iteration steps as: 1. Initialize X [0] as random start configuration, set T = X [0] and k = 0, and compute σ(x [0] ); 2. Increase the k by one; 3. Compute X [k] with the above update formula and σ(x [k] ); 4. If σ(x [k 1] ) σ(x [k] ) < ǫ, which is a small positive constant, then stop; Otherwise set T = X [k] and go to step 2. The ǫ is an empirical threshold based on accuracy requirement. We usually set it as 5% of the average radio range. This algorithm generates the relative positions of sensor nodes in X [k]. The computation complexity of iterative MDS is an O(N 2 ) [11, 69]. The above methods can estimate the relative locations of sensor nodes based on their pairwise distances. We also need position alignment techniques to map the relative coordinates to physical coordinates based on three or more anchor sensors. The alignment techniques will be discussed in the next chapter. 3.4 Ranging Estimation We employ the widely used distance measurement model of Received Signal Strength Indication (RSSI). A circle centered in a sensor node bounds the maximal range for direct communication, which is called the hop distance, of the sensor s radio

55 39 r A r D h ad B r h C Fig Hop distance and signal strength signal. Nodes within one hop distance can directly communicate with each other, while nodes that are in more than one hop away relay messages hop by hop. The power of the radio signal attenuates exponentially with distance, and this property enables the receiver to estimate the distance to the sender by measuring the attenuation in radio signal strength between sender and receiver. For example, there are four sensor nodes A, B, C, and D in Figure 3.1. Hop distance is r h. r ad is the distance between A and D and it can be induced with A s signal strength at location of D. 3.5 Pairwise Distance Collection Usually, a network of sensors are randomly, densely distributed. They are sufficiently connected and previous research indicates the average connection degree of a node is between 5 and 15 in a general sensor network model. The essential operation in pairwise distance collection is flooding by several selected sensor nodes. We describe the procedure as below. An anchor node is selected as source sensor to initialize a broadcast containing its ID, location, and hop count

56 40 r S A B C G F E D Fig Routes of a flooding initialized by node S equal to 0. Each of its one-hop neighbors hears the broadcast, appends its ID to the message, increases the hop count by one, and then rebroadcasts it. Every other node that hears broadcast but did not hear the previous broadcasts with lower hop count will append its ID, increase the hop count by one, and then rebroadcast. The process continues until all nodes in the sensor network get the message broadcasted by the original source node. Each node that is far away from the source node usually keeps a route from source node to it. An example broadcast is illustrated in Figure 3.2, where node S initializes a broadcast and the average hop distance is r. Each route found is indicated with connected arrow lines. Nodes A, B, C, D, E, F, G each keep the corresponding route information from node S to them, respectively. The distance of any pair of nodes on one of the routes can be calculated by multiplying the average hop distance (calculated by following operation) by the number of hop count between them on the route. Usually, a

57 41 source node s broadcast only collects the pairwise distances of nodes for which the route information is available. When there is another anchor node hears the broadcast, it uses the information in the received message to induce the average hop distance. The anchor node is then selected as a new source node and it initializes another broadcast later to collect more pairwise distances as well as publish the average hop distance. Similarly, we can select some other nodes as source nodes to broadcast. For n sensors in a sensor network, there are n(n 1)/2 pairwise distances in total. Our experimental results indicate that a source node broadcasts to all other nodes usually collects 3% 8% of all pairwise distances depending on the relative location of the source node in the network, connection degree of nodes and hop distance. As we have mentioned, the following iterative location algorithm will generate location estimation with various accuracies depending on the percentage of the pairwise distances collected to all pairwise distances. Usually, we need more than 10% pairwise distances collected for an accurate location estimation. Thus, a certain amount of source nodes (anchor nodes or general nodes without location know) should be selected and initialize broadcasts. However, the total number of pairwise distances collected does not increase linearly with the number of source nodes selected, since there are a lot of overlaps among the sets of broadcast routes, which determine the pairwise distance obtained, by every source nodes broadcast. In order to reduce the total number of messages (or power consumption) sent or received by all nodes during source nodes broadcasts in the sensor network, we hope to initialize as few source sensors to broadcast as possible and collect as many pairwise distances as possible. This requires that broadcast from each source sensor can collect

58 42 relatively more pairwise distances and the overlap among sets of pairwise distances collected by every source node s broadcast should be small. Figure 3.3 illustrate a typical network of sensors (dots) and broadcast routes (lines) from a source node (the triangle in the left-up corner). There are 400 sensor nodes, average hop distance 1.2, and 3.1% sensor pairwise distances collected in the network. We take a heuristic analysis of source nodes selection with approximating the topology of a network of sensors with grids. An approximated topology of a sensor network with 37 sensor nodes is plotted in Figure 3.4. Node S initializes the broadcast and the circle centered with S represents the range of signal. Some routes marked by arrow lines are selected to connect 16 nodes, while other routes are omitted. These selected routes contain relatively more nodes than other routes. Based on the route information in nodes A, B, C, D, E, F, G, we induce 34 pairwise distance. With the grid model, we have the observations: 1. A broadcast initialized by a source node located at the outer part of the network usually collects a larger number of pairwise distances than that of a source node located at the inner part of the network; 2. Broadcasts initialized by source nodes geodesic far away from each other tend to generate pairwise distance sets with less overlap. We illustrate the above principle with Figure 3.5 and Figure 3.6. Both of them illustrate broadcast routes from different source nodes on the same sensor network as that in Figure 3.2. The source node in Figure 3.2 and 3.6 is more far away from the center of the network than that in Figure 5. There are 24 pairwise distances collected in Figure 5 and 34 in Figure 4 and 6, respectively. If Figure 4 indicates the first broadcast and

59 Fig Flooding routes from a source node of a sensor network r A B C D E F G S Fig A broadcast initialized by node S collects 34 pairwise distances

60 44 S r A B C G F E D Fig A broadcast initialized by node S collects 24 pairwise distances S r A B C G F E D Fig A broadcast initialized by node S collects 34 pairwise distances

61 45 Figure 5 indicates the second broadcast, then the second broadcast in Figure 5 collect extra 24 pairwise distances, while the broadcast in Figure 6 only collect extra 6 pairwise distances. Thus, during pairwise distance collection, we should select new source node which is far way from most of previous source nodes and the center of the network. 3.6 Performance Study We measure the performance of the algorithm with mean error, which is widely used in previous research works: error = ni=m+1 x i est xi real 2 (n m) (radio range), (3.17) where n and m are the total number of sensors and the number of anchors, respectively. A low error means good performance of the method. During our simulation, 400 nodes are randomly and uniformly placed in a square region of side length 10. If distance of a pair of nodes is less than 1, the nodes are labelled as directly connected. In order to understand how the classic MDS and iterative MDS work, we first study the performance of classic MDS and iterative MDS in recovering sensors position. Figure 3.7(a), (b), and (c) show the procedure of recovering sensors positions within a small area with classical MDS. Sensors A, B, and C are the three anchor senors. The Figure 3.7(c) shows the estimated physical position for all sensors within the area. Figure 3.7(d) indicates that when the error of measured distances for pairwise adjacent sensors increase, the error rates of sensor positioning increases. We vary the density of

62 46 sensor deployment so that different number of sensors are enclosed in the area. When the number of sensors in the area is small, the error rates barely increase even as the measured distance error increases. When there are more sensors in the area, the error rates of sensor positioning increase faster. The increase of error rates under different conditions is always slower than the increase of distance measurement error. This indicates the classical MDS is robust in tolerating measurement errors of sensor distance. Based on the experiments, we get the observation that it is preferred to estimate positions for less number of sensors within a small area, which tends to generate more accurate sensor positioning. Figure 3.8 is the experimental results about recovering sensors location with iterative MDS. When the number of iterations increase, the error rates of sensor localization decrease. But, a large number of iteration steps mean high computation costs and computation time. In Figure 3.8(a), the three curves correspond to error rates with different percentage of pairwise distances collected during sensor localization. When more pairwise distances collected for sensor localization based on iterative MDS, the error rates decrease as well. The error rates of sensor localization with iterative MDS is larger than that with classical MDS. In Figure 3.8(b), when the collected pairwise distance and the number of iteration are fixed, the error rates of sensor localization increase with the increase of distance measurement error. The increase of sensor localization error rates are slower than the increase of distance measurement. This indicates the iterative MDS is also robust in tolerating errors of pairwise sensor distance measurement.

63 A B B A 2 1 C (a) A C sensors (b) sensors 20 sensors 6 B Location error rates C (c) Measured range error (d) Fig (a)the physical positions of sensors in an adjacent area.(b) The recovered relative positions of sensors in the adjacent area based on classical MDS. (c) These sensors physical positions after alignment. (d)when the error of measured distances for pairwise adjacent sensors increases, the error rates of estimated sensor positions increase.

64 all pairwise distance collected 90% pairwise distances collected 70% pairwise distances collected Location error rates Location error rates Number of Interation (a) Range measure error (b) Fig (a)error rates of sensor localization increase when the percentage of sensor pairwise distances collected and the number of iteration increase. (b)when the collected pairwise distance and the number of iteration are fixed, the error rates of sensor localization increase with the increase of distance measurement error.

65 49 We utilize the DV-distance propagation method [70] to control flooding as well as our flooding scheme (hop distance). Simulation results shown in Figure 3.9 are competitive with previous research. 8 7 DV distance hop distance 6 Average Error Percentage of Pairwise Distances Collected Fig Error rates when varying the percentage of collected pairwise distances In order to demonstrate the scheme we proposed for source nodes selection, we compare the number of collected pairwise distances based on random source nodes selection and our selection scheme. The results are shown in Figure 3.10 and indicates that our source nodes selection scheme is efficient in pairwise distance collection. 3.7 Summary In this chapter, we explore the idea of using multidimensional scaling technique to compute relative positions of sensors in a wireless sensor network. A centralized sensor

66 50 Percentage of Collected Pairwise Distances Our selection principle Random selection Number of Source Nodes Fig Percentage of collected pairwise distances when increasing the number of source nodes and broadcasts localization algorithm is proposed to get the accurate position estimation and reduce error cumulation. In order to support the implementation of the algorithm, we also study the pairwise sensor distances collection with flooding.

67 51 Chapter 4 Distributed and Robust Sensor Localization In the chapter, we extend the centralized sensor localization algorithm into a distributed sensor localization algorithm and a robust sensor localization method based on multidimensional scaling technique. In the distributed sensor localization algorithms, multidimensional scaling is used to estimate location of adjacent sensors in small regions to form local maps. Then, these local maps are aligned to form a global map that describe location information of all sensors in the network. In the robust sensor localization algorithm, local maps are calculated for sensor nodes along the flooding route from one anchor sensor to another anchor sensor only. The estimated positions of the anchors are compared with their physical positions and corrected. The positions of other sensors are corrected accordingly. With iterative adjustment, the robust localization algorithm is able to overcome adverse network and terrain conditions, and generate accurate sensor position. 4.1 Distributed Sensor Localization Calculating Relative Positions In our distributed sensor localization method, the above MDS techniques are used in a distributed manner to estimate a local map for each group of adjacent sensors, and

68 52 then these maps are aligned together based on the alignment method. In this section, the details of distributed sensor localization method are presented. We employ the widely used distance measurement model of Received Signal Strength Indication (RSSI). It is necessary to point out that some other distance measure approaches, such as TOA, TDOA, AoA, and Ultrasound, can also be applied here. They even generate more accurate distance measure than RSSI, but they usually need complex hardware equipped in each sensor. In the dissertation, we intend to use RSSI and simple hardware configuration to achieve competitive performance. Based on the analysis of the challenges of sensor localization problem in real applications, the conditions that most existing sensor positioning methods fail to perform well are the anisotropic topology of the sensor networks and complex terrain where the sensor networks are deployed. In order to accurately position sensors in anisotropic network and complex terrain, the distributed sensor localization algorithm computes a series of local maps which are computed with multidimensional scaling. These local maps are then pieced together to get the approximation of the physical positions of the sensor nodes. The method estimates the relative locations of sensor nodes based on their pairwise distances. We also need position alignment techniques to map the relative coordinates to physical coordinates based on three or more anchor sensors Aligning Relative Positions Since we hope to compute the physical positions of sensors eventually, it is necessary to align the relative positions to physical positions with the aid of sensors with

69 positions known. For an adjacent group of sensors, at least three sensors physical positions are needed in order to identify the physical positions of remaining nodes in the group in 2-D case. Thus, each group of adjacent sensors must contain at least three nodes with physical positions known, which may be anchors or nodes with physical positions calculated previously. The alignment usually includes shift, rotation, and reflection of coordinates. R = [r ij ] 2 n = (R 1, R 2,...,R n ) denotes the relative positions of the set of n sensor nodes in 2-dimensional space. T = [t ij ] 2 n = (T 1, T 2,...,T n ) denotes the true positions of the set of n sensor nodes in 2-dimensional space. In following explanation, we assume the nodes 1,2,3 are anchors. A vector R i may be shifted to R (1) i by R (1) i 53 = R i + X, where X = R (1) i R i. It may be rotated counterclockwise through an angle α to R (2) i = Q 1 R i, where Q 1 = cos(α) sin(α) sin(α) cos(α). It may also be reflected across a line S = cos(β/2) sin(β/2) to R (3) i = Q 2 R i, where Q 2 = cos(β) sin(β) sin(β) cos(β).

70 54 Before alignment, we only know R and three or more anchor sensors physical positions T 1, T 2, T 3. Based on them, we computer T 4, T 5,...,T n. Based on the above rules, we have (T 1 T 1, T 2 T 1, T 3 T 1 ) = Q 1 Q 2 (R 1 R 1, R 2 R 1, R 3 R 1 ). (4.1) With R 1, R 2, R 3, T 1, T 2, and T 3 known, we can compute Q = Q 1 Q 2 = (R 1 R 1, R 2 R 1, R 3 R 1 )/(T 1 T 1, T 2 T 1, T 3 T 1 ). (4.2) Then, (T 4, T 5,...,T n ) can be calculated with (T 4 T 1, T 5 T 1,...,T n T 1 ) = Q(R 4 R 1, R 5 R 1,...,R n R 1 ), (4.3) (T 4, T 5,...,T n ) = Q(R 4 R 1, R 5 R 1,...,R n R 1 ) +(T 1, T 1,...,T 1 ). (4.4) 4.2 Robust Sensor Localization An anchor node named as starting anchor initializes flooding to the whole network. When other anchor nodes, named ending anchors, get the flooding message, they

71 55 pass their positions back to the starting anchor along the reverse routes from starting anchor to each of them. Then, the starting anchor knows the positions of ending anchors and routes to each of them. The average radio ranges in different directions from the starting anchor to different ending anchors can be estimated with the hop counts and physical distances between the starting sensor to these anchor sensors. Figure 4.1 shows a flooding initialized by the starting anchor in up-left corner of the square area. Black lines are the routes that the flooding passed, and blue circles represent the adjacent areas where sensors position will be estimated with MDS. Starting Anchor Ending Anchor Fig Flooding from a starting anchor to the whole network. Red nodes are anchor nodes. After the flooding, the starting anchor will initialize sensor localization for sensors along the routes from the starting anchor to each ending anchor.